Abstract. A classical theory is developed for the time development and
scattering of a minimally coupled scalar field on closed spacetimes
that evolve from initial, to final static states. The time
development is obtained by reformulating the field equation as an
abstract Cauchy problem on a Hilbert space. Constraints are imposed
on the metric that enable the use of semigroup theory, and the field
solution is obtained from Cauchy data via application of a two
parameter semigroup of evolution operators. The scattering theory is
also formulated on a Hilbert space, and the wave operators and
scattering operator are constructed from the evolution operators. It
is shown that semigroup theory most readily applies to spacetimes
that undergo contraction.